A Stability Property of Mean Curvature Vectors of Codimension-One Foliations

Name: Work Video:
Duration: 3 min 30 s
Description: In this paper, we show a stability property of mean curvature vector fields of codimension-one foliations with respect to small perturbations of the given codimension-one foliation. This is an extended form of D. Sullivan’s result: If a codimension-one foliation is geometrically taut then any foliation sufficiently close to the foliation is also geometrically taut.
Gen-ichi Oshikiri
{'id': 'https://openalex.org/W2080949138', 'doi': 'https://doi.org/10.4036/iis.2011.45', 'title': 'A Stability Property of Mean Curvature Vectors of Codimension-One Foliations', 'display_name': 'A Stability Property of Mean Curvature Vectors of Codimension-One Foliations', 'publication_year': 2011, 'publication_date': '2011-01-01', 'ids': {'openalex': 'https://openalex.org/W2080949138', 'doi': 'https://doi.org/10.4036/iis.2011.45', 'mag': '2080949138'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.4036/iis.2011.45', 'pdf_url': 'https://www.jstage.jst.go.jp/article/iis/17/1/17_1_45/_pdf', 'source': {'id': 'https://openalex.org/S85999832', 'display_name': 'Interdisciplinary Information Sciences', 'issn_l': '1340-9050', 'issn': ['1340-9050', '1347-6157'], 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310313307', 'host_organization_name': 'Tohoku University', 'host_organization_lineage': ['https://openalex.org/P4310313307'], 'host_organization_lineage_names': ['Tohoku University'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'hybrid', 'oa_url': 'https://www.jstage.jst.go.jp/article/iis/17/1/17_1_45/_pdf', 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5014613556', 'display_name': 'Gen-ichi Oshikiri', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I173009982', 'display_name': 'Iwate University', 'ror': 'https://ror.org/04cd75h10', 'country_code': 'JP', 'type': 'education', 'lineage': ['https://openalex.org/I173009982']}], 'countries': ['JP'], 'is_corresponding': True, 'raw_author_name': 'Gen-ichi OSHIKIRI', 'raw_affiliation_strings': ['FACULTY OF EDUCATION IWATE UNIVERSITY'], 'affiliations': [{'raw_affiliation_string': 'FACULTY OF EDUCATION IWATE UNIVERSITY', 'institution_ids': ['https://openalex.org/I173009982']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5014613556'], 'corresponding_institution_ids': ['https://openalex.org/I173009982'], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 65}, 'biblio': {'volume': '17', 'issue': '1', 'first_page': '45', 'last_page': '48'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10229', 'display_name': 'Geometric Analysis and Curvature Flows', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10229', 'display_name': 'Geometric Analysis and Curvature Flows', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T13080', 'display_name': 'Advanced Differential Geometry Research', 'score': 0.9988, 'subfield': {'id': 'https://openalex.org/subfields/3103', 'display_name': 'Astronomy and Astrophysics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T12396', 'display_name': 'Advanced Differential Equations and Dynamical Systems', 'score': 0.9978, 'subfield': {'id': 'https://openalex.org/subfields/2608', 'display_name': 'Geometry and Topology'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/foliation', 'display_name': 'Foliation (geology)', 'score': 0.95128447}, {'id': 'https://openalex.org/keywords/codimension', 'display_name': 'Codimension', 'score': 0.94996476}], 'concepts': [{'id': 'https://openalex.org/C168425004', 'wikidata': 'https://www.wikidata.org/wiki/Q525802', 'display_name': 'Foliation (geology)', 'level': 3, 'score': 0.95128447}, {'id': 'https://openalex.org/C83979697', 'wikidata': 'https://www.wikidata.org/wiki/Q1778247', 'display_name': 'Codimension', 'level': 2, 'score': 0.94996476}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.75502807}, {'id': 'https://openalex.org/C195065555', 'wikidata': 'https://www.wikidata.org/wiki/Q214881', 'display_name': 'Curvature', 'level': 2, 'score': 0.5298507}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.4964226}, {'id': 'https://openalex.org/C175017881', 'wikidata': 'https://www.wikidata.org/wiki/Q1318998', 'display_name': 'Mean curvature', 'level': 3, 'score': 0.48655024}, {'id': 'https://openalex.org/C189950617', 'wikidata': 'https://www.wikidata.org/wiki/Q937228', 'display_name': 'Property (philosophy)', 'level': 2, 'score': 0.48388016}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.43647522}, {'id': 'https://openalex.org/C112972136', 'wikidata': 'https://www.wikidata.org/wiki/Q7595718', 'display_name': 'Stability (learning theory)', 'level': 2, 'score': 0.42434093}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.32298586}, {'id': 'https://openalex.org/C127313418', 'wikidata': 'https://www.wikidata.org/wiki/Q1069', 'display_name': 'Geology', 'level': 0, 'score': 0.11651629}, {'id': 'https://openalex.org/C119857082', 'wikidata': 'https://www.wikidata.org/wiki/Q2539', 'display_name': 'Machine learning', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C138885662', 'wikidata': 'https://www.wikidata.org/wiki/Q5891', 'display_name': 'Philosophy', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C111472728', 'wikidata': 'https://www.wikidata.org/wiki/Q9471', 'display_name': 'Epistemology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C26687426', 'wikidata': 'https://www.wikidata.org/wiki/Q47069', 'display_name': 'Metamorphic rock', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C17409809', 'wikidata': 'https://www.wikidata.org/wiki/Q161764', 'display_name': 'Geochemistry', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.4036/iis.2011.45', 'pdf_url': 'https://www.jstage.jst.go.jp/article/iis/17/1/17_1_45/_pdf', 'source': {'id': 'https://openalex.org/S85999832', 'display_name': 'Interdisciplinary Information Sciences', 'issn_l': '1340-9050', 'issn': ['1340-9050', '1347-6157'], 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310313307', 'host_organization_name': 'Tohoku University', 'host_organization_lineage': ['https://openalex.org/P4310313307'], 'host_organization_lineage_names': ['Tohoku University'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.4036/iis.2011.45', 'pdf_url': 'https://www.jstage.jst.go.jp/article/iis/17/1/17_1_45/_pdf', 'source': {'id': 'https://openalex.org/S85999832', 'display_name': 'Interdisciplinary Information Sciences', 'issn_l': '1340-9050', 'issn': ['1340-9050', '1347-6157'], 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310313307', 'host_organization_name': 'Tohoku University', 'host_organization_lineage': ['https://openalex.org/P4310313307'], 'host_organization_lineage_names': ['Tohoku University'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 9, 'referenced_works': ['https://openalex.org/W14718745', 'https://openalex.org/W1487638357', 'https://openalex.org/W1527311809', 'https://openalex.org/W1557566490', 'https://openalex.org/W2006880768', 'https://openalex.org/W2085213356', 'https://openalex.org/W2731780461', 'https://openalex.org/W4248136896', 'https://openalex.org/W433096083'], 'related_works': ['https://openalex.org/W4287121837', 'https://openalex.org/W4221157369', 'https://openalex.org/W3212916211', 'https://openalex.org/W3100373151', 'https://openalex.org/W3098035043', 'https://openalex.org/W2984975771', 'https://openalex.org/W2490194852', 'https://openalex.org/W2080949138', 'https://openalex.org/W1996072570', 'https://openalex.org/W1987909324'], 'abstract_inverted_index': {'In': [0], 'this': [1], 'paper,': [2], 'we': [3], 'show': [4], 'a': [5, 36], 'stability': [6], 'property': [7], 'of': [8, 13, 21, 31], 'mean': [9], 'curvature': [10], 'vector': [11], 'fields': [12], 'codimension-one': [14, 24, 37], 'foliations': [15], 'with': [16], 'respect': [17], 'to': [18, 47], 'small': [19], 'perturbations': [20], 'the': [22, 48], 'given': [23], 'foliation.': [25], 'This': [26], 'is': [27, 39, 50], 'an': [28], 'extended': [29], 'form': [30], 'D.': [32], 'Sullivan’s': [33], 'result:': [34], 'If': [35], 'foliation': [38, 44, 49], 'geometrically': [40, 52], 'taut': [41], 'then': [42], 'any': [43], 'sufficiently': [45], 'close': [46], 'also': [51], 'taut.': [53]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2080949138', 'counts_by_year': [], 'updated_date': '2024-12-13T21:48:19.416670', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
